Question

Four forces, 60N at 60^o and 50N at 30^o both clockwise, 40N due north – west and 30N south – west, act at the origin. Calculate the magnitude and direction of the resultant force.

Answer 1

$F_x=-40\cdot\cos45°-30\cdot\cos45°+50\cdot\sin30°+60\cdot\sin60°=$

$=52\ (N)$

$F_y=40\cdot\sin45°-30\cdot\sin45°+50\cdot\cos30°+60\cdot\cos60°=$

$=80.4\ (N)$

$F=\sqrt{52^2+80.4^2}=96\ (N)$ . Answer

$\alpha=\tan^{-1}\frac{80.4}{57.1}=57.1°$ North of East . Answer